Surjection

This article/section deals with mathematical concepts appropriate for a student in mid to late high school.

A surjection or surjective function is a mapping (or function) between two sets, that is "onto". This means that the function "hits" every point in the range. That is, no point in the range isn't mapped to.

In other words, a surjection from set A to set B is a mapping such that every element in B has some element in A mapped to it. For example, one surjection between the sets {X, Y, Z} and {1, 2}, maps: X to 1, Y to 2, and Z also to 2. If we were use this map instead: X to 1, Y to 1, and Z to 1, it would fail to be "onto" because nothing maps to 2.